variables not being saved?
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Hi @Olivia,
I have updated both functions. The updated provided code consists of two functions: lumine and lusolver.The lumine function performs the LU decomposition of a given coefficient matrix A and returns the lower matrix L and upper matrix U. It follows the following steps:Checks if the matrix A is square. If not, it throws an error and also if the matrix A is singular. If yes, it throws an error.Then, it initializes L as an identity matrix and U as A.Performs the LU decomposition using nested loops.Updates the rows of U and store the factors in L and sets the diagonal elements of L to 1.The lusolver function takes the lower matrix L, upper matrix U, and a vector B as inputs and solves the system of linear equations using LU decomposition. It follows the following steps:Initializes vectors y and x with zeros., performs forward substitution to solve Ly = B and backward substitution to solve Ux = y. Afterwards, returns the solution vector x.
Lumine Function
function [L,U] = lumine(A)
% lumine: LU decomposition
% input:
% A = coefficient matrix
% output:
% L = lower matrix
% U = upper matrix
[m,n] = size(A); % defines m and n
if m ~= n % checks if the matrix is square
error('Matrix A must be square');
end
if det(A) == 0 % checks if the matrix is singular
error('Matrix cannot be singular');
end
% Initialize L as an identity matrix and U as A
L = eye(n);
U = A;
for k = 1:n % starts at position 1, goes to the last column for i = k+1:n % starts at row after k, goes to second to last row
factor = U(i,k)/U(k,k); % defines factor
U(i,k:n) = U(i,k:n) - factor * U(k,k:n); % update row i of U
L(i,k) = factor; % store factor in L
end
end
% The diagonal of L should be set to 1 (identity property) for i = 1:n
L(i,i) = 1;
end
end
q = [2 1 -1; 4 0 2; 8 1 0];
[L,U] = lumine(q); % Now both L and U will be defined correctly.
disp('Matrix L:');
disp(L); % Display the lower matrix L
disp('Matrix U:');
disp(U); % Display the upper matrix U
Lusolver function
function solution = lusolver(L, U, B)
n = length(B);
y = zeros(n, 1);
x = zeros(n, 1);
% Forward Substitution (Ly = B)
for i = 1:n
y(i) = B(i) - L(i,1:i-1)*y(1:i-1);
end
% Backward Substitution (Ux = y)
for i = n:-1:1
x(i) = (y(i) - U(i,i+1:n)*x(i+1:n)) / U(i,i);
end
solution = x;
end
B = [-1;-2;-3];
solution = lusolver(L,U,B);
disp(solution);
Please see attached.
![](/matlabcentral/answers/uploaded_files/1750589/IMG_7399.jpeg)
![](/matlabcentral/answers/uploaded_files/1750594/IMG_7398.jpeg)
Hope, after this detailed explanation and provided two updated functions, your problem is resolved. Please let me know if you still have any further questions.
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